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The topological property of boson-fermion mixture in a one-dimensionaloptical superlattice is studied and the topological insulating phase ofinteracting boson-fermion mixture characterized by a nontrivial Berry phase isidentified. The single-particle and boson-fermion exchanging excitationspectrums are calculated and we identify the boson-fermion exchangingexcitation as the gapless topological excitation in the topological phase ofthe mixture. The different kinds of excitations are explained explicitly fromthe competition among the bulk gap, the on-site boson-boson and boson-fermioninteractions. The Hamiltonian studied has been partly realized in thestate-of-art cold atom experiments, and the results are very relevant to theexperiments.

The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures